Homogenous differential equation

[powersys]

homogenous de

Why do we use 'homogenous' to describe a differential equation?

From Cambridge Dictionary:
homogeneous
adjective (ALSO homogenous)
consisting of parts or people which are similar to each other or are of the same type

 

[Mr. Notorious]

homogenous differential equation

It's when the powers of the function are all the same, homogenous.

For example...

x^2 -3xy+4y^2 is homegenous because each term is to the second degree.

 

[powersys]

It's when the powers of the function are all the same, homogenous.

For example...

x^2 -3xy+4y^2 is homegenous because each term is to the second degree.

Do u mean 'xy' also considered to have 2nd degree/order?

 

[cclogan]

a homogeneous DE is when the equation is equal to zero. For example:
y' + 2y = 0 ( if there was a constant or another term in the equation there it would not be equivalent to zero)
the formal definition (for a first order) would be:

y'+ p(t) * y = 0, where p(t) is a function dependent on t

example of non-homogeneous

y'+2y=2t
y''+3y'+2y=3

so you are only using homogeneous to describe certain differential equations, not all of them

 

[alisha]

its accurate defintion can b

if each term of a differential eqn contains whether da derivative or da dependent function den its called homogenous differntial eqn.

Added after 1 minutes:

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[uahee]

A homogenous DE is when the function is equal to zero.

 

[voyageoflife]

this is done because of the ease of calculations. direct solutions to diffrential equations are difficult . when we describe any equation as a combination of homogeneous solution and particular solution it makes or job very easy.
equating to zero makes it like a quadratic which is easy to solve and then for the constants we go for the particular solution.

hope this got ya.. most og the methods used in mathematics are done because they make our jobs easier.. that is why we use all these transforms and sutff also.

 

[edata]

Hi all,
Homogenous equation is the differential equation which is sum is equal to 0.
Answer for why do we sepearte diff eq is for solving purposes and also these equations with their form have physical interpretation. For ex. a homogeneous equation shows a systems equilibrium point.